The initial question was why all the files in minification have the "Pending" status and that doesn't change for hours while on other sites it lasts no more than a couple of minutes.
After putting CDN into "Dev" mode (to bypass it) and purging cache, I can't even enable minification again. The server is using Nginx + Redis cache and I suppose that cache is related but I might be missing something. Unfortunately, this cache cannot be disabled. Is there any solution for this?